Alladi, K., Chair; White, N., Associate Chair; Alladi, K.; Bao, G.; Block, L.S.; Boyland, P.L.; Brechner, B.L.; Brooks, J.K.; Cenzer, D.S.; Cheah, J.L.; Chen, Y.; Crew, R.M.; Dinculeanu, N.; Drake, D.A.; Dranishnikov, A.N.; Edwards, B.H.; Ehrlich, P.E.; Emch, G.G.; Garvan, F.G.; Groisser, D.J.; Hager, W.W.; Ho, C.Y.; Hueter, I.; Keating, K.P.; Keesling, J.E.; Kellum, M.; Khuri, R.L.; King, J.L.; Klauder, J.R.; Larson, J.A.; Martinez, J.; McCracken, D.L.; McCullough, S.A.; Mitchell, W.J.; Moore, T.O.; Moskow, S.; Olson, T.E.; Pop-Stojanovic, Z.R.; Rao, M.K.; Robinson, P.L.; Saxon, S.A.; Shen, L.C.; Sin, P.K.; Smith, J.Y.; Stark, C.W.; Summers, S.J.; Thompson, J.G.; Tiep, P.H.; Tornwall, S.B.; Townsend, M.D.; Turull, A.; Vince, A.J.; Voelklein, H.K.; Walsh, T.; White, N.L.; Wilson, D.C.

Undergraduate Coordinator: Rick Smith

Actuarial Science Advisers:

Bruce Edwards, 364 Little Hall, 392-0281 ext 281; be@math.ufl.edu

Dennis Wackerly, 220 FLO, 392-1941 ext 227; dwack@stat.ufl.edu

David Nye, 329 BUS, 392-0153;
dnye@dale.cba.ufl.edu

Graduate Coordinator: Paul Robinson

Office: 358 Little (392-0281)

www.math.ufl.edu

Review of limits, differentiation and integration; calculus of vector functions; line and surface integration; calculus of variations; Fourier series. Material presented with view to applications. GR-M†

A continuation of MAA 4102. GR-M†

An advanced treatment of limits, differentiation, integration, series; calculus of functions of several variables. GR-M†

A continuation of MAA 4211. GR-M†

Topology of metric spaces, numerical sequences and series, continuity, differentiation, the Riemann-Stielties integral, sequences and series of functions, the Stone-Weierstrass, theorem, functions of several variable, Stokes’ theorem, the Lebesgue theory. GR-M†

A continuation of MAA 4226. GR-M†

Complex numbers, analytic functions, Cauchy-Riemann equations, harmonic functions, elementary functions, integration, Cauchy-Goursat theorem, Cauchy integral formula, infinite series, residues and poles, conformal mapping. Mathematics: calculus and precalculus. GR-M†

NOTE: A student can receive at most four hours credit for both MAC 1147 and MAC 1140 and at most four credits for MAC 1147 and MAC 1114. At most five credit hours for MAC 1147,MAC 1140 and MAC 1114. "Credit" means credit toward graduation, general education, basic distribution, or Gordon Rule.

Exponential and logarithmic functions, trigonometry, analytic and additional applications of trigonometry. (M) (See note above) GR-M†

College algebra, functions, coordinate geometry, exponential and logarithmic functions. (M) (See note above) GR-M†

College algebra, functions, coordinate geometry, exponential and logarithmic functions, and trigonometry. This fast-paced course is designed as a review of algebra and trigonometry to prepare the student for calculus. This course assumes prior knowledge of intermediate algebra (Algebra II). (M) (See note above) GR-M†

A geometric and heuristic approach to calculus; differentiation and integration of simple algebraic and exponential functions, applications to graphing, marginal analysis, optimization, areas and volumes. (M) GR-M†

Sequences, geometric and Taylor series; systems of linear equations, Gaussian elimination, matrices, determinants and vectors; partial differentiation, multiple integrals; applications to marginal analysis, least-squares and Lagrange multipliers. (M) GR-M†

Introduction to analytic geometry; limits; continuity; differentiation of algebraic and trigonometric functions, differentials; introduction to integration and the fundamental theorem of calculus. (M) (Credit will be given for at most one of MAC 2311 and MAC 3472.) GR-M†

Techniques of integration; applications of integration; differentiation and integration of inverse trigonometric, exponential and logarithmic functions; sequences and series. (M) (Credit will be given for at most one of MAC 2312, MAC 3512, and MAC 3473.) GR-M†

Solid analytic geometry; vectors; partial derivatives; multiple integrals. (M) (Credit will be given for at most one of MAC 2313 and MAC 3474.) GR-M†

A first course in calculus for students who enjoy and have a sound background in mathematics. The topics covered in the sequences MAC 3472-3-4 closely parallel those covered in MAC 2311-2-3 but are treated in greater depth. (M) (Credit will be given for at most one of MAC 2311 and MAC 3472.) GR-M†

A continuation of MAC 3472. (M) (Credit will be given for at most one of MAC 2312, MAC 3512, and MAC 3473.) GR-M†

A continuation of MAC 3473. (M) (Credit will be given for at most one of MAC 2313 and MAC 3474.) GR-M†

A calculus course for entering freshmen who have Advanced Placement credit for MAC 2311. The content of MAC 2311 and 2312 is covered: limits, continuity, differentiation, applications of differentiation, integration, logarithms and exponential functions, applications of integration, techniques to integration, sequences, series, conic sections and parametric equations. The content of the AP syllabus is reviewed during the first half of the semester, and there is a special emphasis on topics not in the AP Calculus AB syllabus, such as infinite series. (M) (Credit will be given for at most one of MAC 2312, MAC 3512, and MAC 3473.) GR-M†

Permutations and combinations, binomial coefficients, inclusion-exclusion, recurrence relations, Fibonacci sequences, generating functions, graph theory. (M) GR-M†

Matching theory, block designs, finite projective planes and error-correcting codes. This course can be taken without taking MAD 4203. (M) GR-M†

Numeric integration, nonlinear equations, linear and non-linear systems of equations, differential equations and interpolation. GR-M†

Finite and infinite state machines; Turing machines, formal languages and their recognition automata; recursive functions; decidability and unsolvability; halting problem; space-time tradeoff. (M) GR-M†

Properties and operations of rational numbers, ratio, proportion, percent, an introduction to real numbers, elementary algebra, informal geometry and measurement, and an introduction to probability and descriptive statistics.

First order differential equations, theory of linear differential equations, solution of linear equations with constant coefficients, the Laplace transform, solution of equation by the Laplace transform. (M) GR-M†

Random walks and Poisson processes, martingales, Markov chains, Brownian motion, stochastic integrals and Ito’s formula. GR-M†

Series solutions of differential equations, Sturm-Liouville Systems. GR-M†

Origin and solution of partial differential equations by various methods including Lagrange linear equations; elementary partial equations of mathematical physics. GR-M†

Complex variables, including derivatives and integrals, singularities, Taylor/Laurent series and residues; Linear Algebra, including Gaussian elimination, determinants, inversion, linear independence, QR decomposition, eigenvalues and eigenvectors, systems of differential equations; (time permitting) Numerical methods, including roots of equations, numerical integration and numerical optimization.

Introduction to linear systems and transforms, Laplace, Fourier and Z transforms and their mutual relationship, convolutions. Operational calculus, computational methods including the fast Fourier transform, second order stationary process, their autocorrelation functions, and problems of interpolation, extrapolation, filtering and smoothing or second order stationary processes. GR-M†

Linear equations, matrices and determinants. Vector spaces and linear transformations. Inner products and eigenvalues. This course emphasizes computational aspects of linear algebra. (M) GR-M†

Algebraic and order properties of the real numbers, introduction to number theory, rational numbers and their decimal expansions, uncountability of the real numbers, complex numbers, irreducible polynomials over the integral, rational, real and complex numbers, elementary theory of equations. This course is particularly useful for prospective secondary school mathematics teachers. (M) GR-M†

Linear equations, matrices, vector spaces, linear transformations, determinants, eigenvalues, inner product spaces. This course is more proof-oriented than MAS 3114. GR-M†

Further topics in linear algebra.

Topics in linear algebra most useful in applications with emphasis on the numerical methods involved: direct and iterative solutions to systems of linear equations, matrix norms, Householder transformations, singular value decomposition, least squares and the generalized inverse, QR method for computing eigenvalues, condition of linear systems and eigensystems. GR-M†

Review of vector algebra, lines, planes and space curves; vector fields, their divergence and curl; line surface and volume integrals including the Divergence Theorem and Stokes’ Theorem. GR-M†

An introduction to elementary number theory and its applications to computer science and cryptology; divisibility, primes, Euclidean Algorithm, congruences, Chinese Remainder Theorem, Euler-Fermat Theorem, primitive roots. Selected applications to decimal fractions, continued fractions, computer file storage and hashing functions, and public-key cryptography. (M) GR-M†

Sets and mappings, groups and subgroups, homomorphisms and isomorphisms, permutations, rings and domains, arithmetic properties of domains, fields. The course involves learning to prove theorems.

GR-M†

Further topics in abstract algebra. GR-M†

For special topics not obtainable in the regular course offerings. GR-M†

Credits: 1 to 3; Prereq: Permission of a departmental adviser. May be repeated for credit. Maximum of 16 credits. GR-M†

Practical co-op work experience as administered through the Cooperative Education Program of the Career Resource Center and coordinated by the mathematics department Cooperative Education Adviser. GR-M†

A general education course which includes an introduction to logic and set theory, algebra, probability and statistics, an elementary introduction to linear programming and game theory, and a review of geometry and measurement. (M) GR-M†

Examples of sets, operations on sets, set algebra, Venn diagrams, truth tables, tautologies, applications to mathematical arguments and mathematical induction. (M) GR-M†

The basic axioms and concepts of set theory. Students present proofs. GR-M†

Models and proofs. Foundations of the real and natural numbers, algorithms, Turing machines, undecidability and independence. Examples and applications in algebra, analysis, geometry and topology. GR-M†

An introduction of mathematics. The course includes a historical discussion of selected mathematical topics. (M)

GR-M†)

A systematic study of the axiomatic structure of Euclidean geometry, including a comparison of the metric (Birkhoff) and synthetic (Hilbert) developments of absolute geometry; parallelism, similarity, area, lines and planes in space, solid mensuration. This course is particularly useful for prospective secondary school mathematics teachers. (M)

GR-M†

The basic concepts of general topology. GR-M†

Continuation of MTG 4302. GR-M†